Method and apparatus for unsupervised training of input synapses of primary visual cortex simple cells and other neural circuits

ABSTRACT

Certain aspects of the present disclosure present a technique for unsupervised training of input synapses of primary visual cortex (V1) simple cells and other neural circuits. The proposed unsupervised training method utilizes simple neuron models for both Retinal Ganglion Cell (RGC) and V1 layers. The model simply adds the weighted inputs of each cell, wherein the inputs can have positive or negative values. The resulting weighted sums of inputs represent activations that can also be positive or negative. In an aspect of the present disclosure, the weights of each V1 cell can be adjusted depending on a sign of corresponding RGC output and a sign of activation of that V1 cell in the direction of increasing the absolute value of the activation. The RGC-to-V1 weights can be positive and negative for modeling ON and OFF RGCs, respectively.

BACKGROUND

1. Field

Certain aspects of the present disclosure generally relate to neuralsystem engineering and, more particularly, to a method and apparatus forunsupervised training of input synapses of primary visual cortex cellsand other neural circuits.

2. Background

Image recognition and motion detection systems can be divided into thosebased on machine vision (i.e., Artificial Intelligence (AI)) techniquesand those utilizing visual cortex techniques (i.e., biologicallyplausible systems). The machine vision systems have well establishedmethods of training, but poor recognition accuracy. For example,distinguishing a dog from a cat remains a challenging task for machinevision systems with a 50/50 outcome.

On the other hand, biologically plausible systems use a human visualcortex structure. Methods based on these systems promise to be moreaccurate than the machine vision systems. However, the training methodsfor biologically plausible systems that lead to their self-organizationare not well developed. This is due to a poor understanding of thevisual cortex organization and self-training methods.

SUMMARY

Certain aspects of the present disclosure provide an electrical circuit.The electrical circuit generally includes a plurality of RetinalGanglion Cell (RGC) circuits, wherein each of the RGC circuitsgenerates, at an output, a sum of weighted inputs from receptor circuitsassociated with that RGC circuit, a plurality of primary visual cortexcell (V1) circuits, wherein each of the V1 circuits generates anothersum of weighted outputs of a subset of the RGC circuits, and a circuitconfigured to adjust weights applied on the outputs for generating theother sum, wherein the adjustment of one of the weights is based on atleast one of one of the outputs on which that weight is applied or theother sum.

Certain aspects of the present disclosure provide a method forimplementing a neural system. The method generally includes generating,at an output of each Retinal Ganglion Cell (RGC) circuit of a pluralityof RGC circuits in the neural system, a sum of weighted inputs fromreceptor circuits associated with that RGC circuit, generating, by eachprimary visual cortex cell (V1) circuit of a plurality of V1 circuits inthe neural system, another sum of weighted outputs of a subset of theRGC circuits, and adjusting weights applied on the outputs forgenerating the other sum, wherein the adjustment of one of the weightsis based on at least one of one of the outputs on which that weight isapplied or the other sum.

Certain aspects of the present disclosure provide an apparatus. Theapparatus generally includes means for generating, at an output of eachRetinal Ganglion Cell (RGC) circuit of a plurality of RGC circuits inthe apparatus, a sum of weighted inputs from receptor circuitsassociated with that RGC circuit, means for generating, by each primaryvisual cortex cell (V1) circuit of a plurality of V1 circuits in theapparatus, another sum of weighted outputs of a subset of the RGCcircuits, and means for adjusting weights applied on the outputs forgenerating the other sum, wherein the adjustment of one of the weightsis based on at least one of one of the outputs on which that weight isapplied or the other sum.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above-recited features of the presentdisclosure can be understood in detail, a more particular description,briefly summarized above, may be had by reference to aspects, some ofwhich are illustrated in the appended drawings. It is to be noted,however, that the appended drawings illustrate only certain typicalaspects of this disclosure and are therefore not to be consideredlimiting of its scope, for the description may admit to other equallyeffective aspects.

FIG. 1 illustrates an example neural system in accordance with certainaspects of the present disclosure.

FIG. 2 illustrates an example model of receptors connected withdifferent types of Retinal Ganglion (RG) cells in accordance withcertain aspects of the present disclosure.

FIG. 3 illustrates an example model of receptors connected with an RGcell that may be ON-cell or OFF-cell depending on a sign of synapseconnecting the RG cell and a primary visual cortex (V1) cell inaccordance with certain aspects of the present disclosure.

FIG. 4 illustrates an example model of connection between receptors andan RG cell, and an example model of connection between RG cells and a V1cell in accordance with certain aspects of the present disclosure.

FIG. 5 illustrates example operations that may be performed at a neuralsystem for training of synapse weights between RG cells and a V1 cell inaccordance with certain aspects of the present disclosure.

FIG. 5A illustrates example components capable of performing theoperations illustrated in FIG. 5.

DETAILED DESCRIPTION

Various aspects of the disclosure are described more fully hereinafterwith reference to the accompanying drawings. This disclosure may,however, be embodied in many different forms and should not be construedas limited to any specific structure or function presented throughoutthis disclosure. Rather, these aspects are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of the disclosure to those skilled in the art. Based on theteachings herein one skilled in the art should appreciate that the scopeof the disclosure is intended to cover any aspect of the disclosuredisclosed herein, whether implemented independently of or combined withany other aspect of the disclosure. For example, an apparatus may beimplemented or a method may be practiced using any number of the aspectsset forth herein. In addition, the scope of the disclosure is intendedto cover such an apparatus or method which is practiced using otherstructure, functionality, or structure and functionality in addition toor other than the various aspects of the disclosure set forth herein. Itshould be understood that any aspect of the disclosure disclosed hereinmay be embodied by one or more elements of a claim.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any aspect described herein as “exemplary”is not necessarily to be construed as preferred or advantageous overother aspects.

Although particular aspects are described herein, many variations andpermutations of these aspects fall within the scope of the disclosure.Although some benefits and advantages of the preferred aspects arementioned, the scope of the disclosure is not intended to be limited toparticular benefits, uses or objectives. Rather, aspects of thedisclosure are intended to be broadly applicable to differenttechnologies, system configurations, networks and protocols, some ofwhich are illustrated by way of example in the figures and in thefollowing description of the preferred aspects. The detailed descriptionand drawings are merely illustrative of the disclosure rather thanlimiting, the scope of the disclosure being defined by the appendedclaims and equivalents thereof.

An Example Neural System

FIG. 1 illustrates an example neural system 100 with multiple levels ofneurons in accordance with certain aspects of the present disclosure.The neural system 100 may comprise a level of neurons 102 connected toanother level of neurons 106 though a network of synaptic connections104. For simplicity, only two levels of neurons are illustrated in FIG.1, although more levels of neurons may exist in a typical neural system.

As illustrated in FIG. 1, each neuron in the level 102 may receive aninput signal 108 that may be generated by a plurality of neurons of aprevious level (not shown in FIG. 1). The signal 108 may represent aninput current of the level 102 neuron. This current may be accumulatedon the neuron membrane to charge a membrane potential. When the membranepotential reaches its threshold value, the neuron may fire and generatean output spike to be transferred to the next level of neurons (e.g.,the level 106).

The transfer of spikes from one level of neurons to another may beachieved through the network of synaptic connections (or simply“synapses”) 104, as illustrated in FIG. 1. The synapses 104 may receiveoutput signals (i.e., spikes) from the level 102 neurons, scale thosesignals according to adjustable synaptic weights w₁ ^((i,i+1)), . . . ,w_(P) ^((i,i+1)) (where P is a total number of synaptic connectionsbetween the neurons of levels 102 and 106), and combine the scaledsignals as an input signal of each neuron in the level 106. Every neuronin the level 106 may generate output spikes 110 based on thecorresponding combined input signal. The output spikes 110 may be thentransferred to another level of neurons using another network ofsynaptic connections (not shown in FIG. 1).

The neural system 100 may be emulated by an electrical circuit andutilized in a large range of applications, such as image and patternrecognition, machine learning, motor control, and alike. Each neuron inthe neural system 100 may be implemented as a neuron circuit. The neuronmembrane charged to the threshold value initiating the output spike maybe implemented, for example, as a capacitor that integrates anelectrical current flowing through it.

In an aspect, the capacitor may be eliminated as the electrical currentintegrating device of the neuron circuit, and a smaller memristorelement may be used in its place. This approach may be applied in neuroncircuits, as well as in various other applications where bulkycapacitors are utilized as electrical current integrators. In addition,each of the synapses 104 may be implemented based on a memristorelement, wherein synaptic weight changes may relate to changes of thememristor resistance. With nanometer feature-sized memristors, the areaof neuron circuit and synapses may be substantially reduced, which maymake implementation of a very large-scale neural system hardwareimplementation practical.

The present disclosure proposes a simplified structure of primary visualcortex (V1) cells and retinal ganglion cells (RGCs) utilized for colorvision, wherein the V1 cells and RGCs may be implemented as neuroncircuits of the neural system 100 from FIG. 1. In an aspect of thepresent disclosure, the RGCs may correspond to the neurons 102, and theV1 cells may correspond to the neurons 106.

V1 input synapses (e.g., the synapses 104 of the neural system 100) mayrequire to be trained in an unsupervised manner to achieve a simple cellemergence. The present disclosure proposes an efficient method oftraining connectivity between V1 and RGC layers of cells that may leadto an autonomous formation of feature detectors (simple cells) withinthe V1 layer. The proposed approach may enable a hardware-efficient andbiological-plausible implementation of image recognition and motiondetection systems.

The proposed unsupervised training method may utilize simple neuronmodels for both RGC and V1 layers. The model simply adds weighted inputsof each cell, wherein the inputs may have positive or negative values.The resulting weighted sums of inputs is called activations, wherein theactivations may also be positive or negative. In an aspect of thepresent disclosure, the weights of each V1 cell may be adjusteddepending on a sign of corresponding RGC output and a sign of activationassociated with that V1 cell in the direction of increasing the absolutevalue of activation. The V1 weights may be positive or negative.

The proposed training method of synapse weights may be suitable forefficient implementation in software and hardware. Furthermore, it mayrun much faster that the Spike Timing Dependant Plasticity (STDP)training approach.

Unsepervised Training Method of Input Synapses of Primary Visual CortexCells

According to certain aspects, RG cells (RGCs) may be divided intoON-cells and OFF-cells. The ON-cells can distinguish objects that arebrighter than a background. For example, peripheral vision is all basedon ON-cells, so that humans can better see bright spots against a darkbackground. On the other hand, RG OFF-cells can distinguish objects thatare darker than a background. It should be noted that illuminating theentire receptive field comprising both RG ON-cells and RG OFF-cells hasa limited effect on an RGC firing rate.

FIG. 2 illustrates an example model 200 a of connection betweenphoto-receptors 202 and an RG ON-cell 204, and an example model 200 b ofconnection between photo-receptors 206 and an RG OFF-cell 208 inaccordance with certain aspects of the present disclosure. The receptorcircuits 202 and 206 may be organized as orthogonal arrays of imagepixels. Therefore, receptive fields of ON- and OFF-cells may have arectangular shape (instead of circular).

In an aspect, each RGC may receive input from nine receptors, whereininput weights associated with the receptors may form a Laplacian filter(i.e., a Laplacian window function may be applied on signals from thereceptors), as illustrated in FIG. 2. The weights may depend on whetherthe receptors are connected to ON- or OFF-RG cells, as illustrated inthe models 200 a and 200 b. It should be noted that the RG cells 204 and208 illustrated in FIG. 2 may not correspond to magno-ganglion cells,which are being able to receive inputs from a much larger number ofreceptors.

In an aspect of the present disclosure, instead of mixing ON- andOFF-cells in an RGC array, each RG cell (e.g., an RG cell 304 receivinginputs from receptors 302 in a model 300 illustrated in FIG. 3) may beeither ON or OFF cell. This may depend on a sign of weight 306associated with a synapse 308 connecting the RG cell 304 to a V1 simplecell 310.

As illustrated in FIG. 3, an input y of the V1 cell 310 may be obtainedby applying a weight w on input signals x_(i,j) from the receptors 302that may be input into the RG cell 304:

$\begin{matrix}{y = {w \cdot {\left( {x_{0,0} - {{1/8} \cdot {\sum\limits_{i = {- 1}}^{+ 1}{\sum\limits_{\underset{{{{i \neq 0}\&}j} \neq 0}{j = {- 1}}}^{+ 1}x_{i,j}}}}} \right).}}} & (1)\end{matrix}$Equation (1) may be rewritten as:

$\begin{matrix}{{y = {{w} \cdot \left( {{{{sgn}(w)}x_{0,0}} - {{1/8} \cdot {{sgn}(w)} \cdot {\sum\limits_{i = {- 1}}^{+ 1}{\sum\limits_{\underset{{{{i \neq 0}\&}j} \neq 0}{j = {- 1}}}^{+ 1}x_{i,j}}}}} \right)}},} & (2)\end{matrix}$wherein if sgn(w)=+1 then the RGC 304 may operate as an ON-cell, and ifsgn(w)=−1 then the RGC 304 may operate as an OFF-cell.

In an aspect of the present disclosure, a neuron model as the oneillustrated in FIG. 4 may be utilized. In an example model 400 a, an RGC404 may sum its weighted inputs 406 from receptors 402, and then it maytransfer the summation result to its output 408, i.e.:

$\begin{matrix}{y = {\sum\limits_{i,j}{u_{i,j} \cdot {x_{i,j}.}}}} & (3)\end{matrix}$

As illustrated in an example model 400 b in FIG. 4, a V1 cell 414 maysum its weighted inputs 416 from RGCs 412, i.e.:

$\begin{matrix}{{z = {\sum\limits_{i,j}{w_{i,j} \cdot y_{i,j}}}},} & (4)\end{matrix}$where each of the weights w_(i,j) from equation (4) may be bipolar formodeling both ON and OFF RGCs. In an aspect, an output 418 (activationsignal) of the V1 cell 414 may be compared with a threshold. If thesummation result 418 is above the threshold, then the V1 cell 414 isactivated (i.e., fires). On the other hand, if the result 418 is belowthe threshold, then the V1 cell 414 is resting.

In an aspect of the present disclosure, only weights of RGC-to-V1connections (i.e., the weights w_(i,j)) may be trained. The model 400 bfrom FIG. 4 may utilize the following rule. The activation of each V1simple cell may be calculated as the weighted sum of the correspondingRGC outputs. If the V1-cell activation exceeds a threshold, then the V1cell may fire. Otherwise, the V1 cell may rest (i.e., the V1 cell doesnot generate any signal) and its input weights may not change.

First, the activation of each V1 simple cell may be calculated as theweighted sum of the corresponding RGC outputs. Then, the weights of eachV1 cell may be adjusted depending on a sign of corresponding RGC outputand a sign of activation of that V1 cell activation. In an aspect, ifthe sign of RGC output and the sign of activation are same, then apositive increment may be added to a weight applied on the RGC output(i.e., the weight may be increased). In another aspect, if the sign ofRGC output and the sign of activation are not same, then a positiveincrement may be subtracted from the corresponding weight (i.e., theweight may be decreased).

For RGC outputs y_(i,j), an activation of V1 cell may be determined asdefined by equation (4). Then, in an aspect of the present disclosure,RGC-to-V1 weights may be adjusted as:w _(i,j) ^(new) =w _(i,j) ^(old) +sgn(y _(i,j))·sgn(z)·|Δw|.  (5)

In another aspect of the present disclosure, the RGC-to-V1 weights maybe adjusted based on a value of the activation instead of its sign,i.e.:w _(i,j) ^(new) =w _(i,j) ^(old) +sgn(y _(i,j))·z·|Δw|.  (6)

The value of |Δw| from equations (5)-(6) may be pre-determined. In anaspect, the value of |Δw| may be in the form of 1/2^(N), where N may bean integer. Since the activation value z may be represented as a binarynumber, the product z·|Δw| from equation (6) may be implemented byperforming a binary shift operation on the value |Δw|.

FIG. 5 illustrates example operations 500 that may be performed at aneural system for training of synapse weights between RG cells and V1cells in accordance with certain aspects of the present disclosure. At502, at an output of each Retinal Ganglion Cell (RGC) circuit of aplurality of RGC circuits in the neural system, a sum of weighted inputsfrom receptor circuits associated with that RGC circuit may begenerated. At 504, each primary visual cortex cell (V1) circuit of aplurality of V1 circuits in the neural system may generate another sumof weighted outputs of a subset of the RGC circuits. At 506, weightsapplied on the outputs for generating the other sum may be adjusted,wherein the adjustment of one of the weights may be based on at leastone of one of the outputs on which that weight is applied or the othersum.

To summarize, instead of mixing ON- and OFF-cells in the RGC layer, itis proposed in the present disclosure to make them all ON/OFF cells andto control their type through the sign of the RGC-to-V1 weights. Simple“add” neurons may be utilized as RG cells, while “add-and-fire” neuronsmay be utilized as V1 simple cells, as illustrated in FIG. 4. Theproposed learning rule for RGC-to-V 1 weights defined by equations(5)-(6) may be applied instead of the STDP learning rule. In an aspectof the present disclosure, the weights may be allowed to change frompositive (modeling a connection to ON RG cell) to negative (modeling aconnection to OFF RG cell), and vice versa.

The various operations of methods described above may be performed byany suitable means capable of performing the corresponding functions.The means may include various hardware and/or software component(s)and/or module(s), including, but not limited to a circuit, anapplication specific integrate circuit (ASIC), or processor. Generally,where there are operations illustrated in Figures, those operations mayhave corresponding counterpart means-plus-function components withsimilar numbering. For example, operations 500 illustrated in FIG. 5correspond to components 500A illustrated in FIG. 5A.

As used herein, the term “determining” encompasses a wide variety ofactions. For example, “determining” may include calculating, computing,processing, deriving, investigating, looking up (e.g., looking up in atable, a database or another data structure), ascertaining and the like.Also, “determining” may include receiving (e.g., receiving information),accessing (e.g., accessing data in a memory) and the like. Also,“determining” may include resolving, selecting, choosing, establishingand the like.

As used herein, a phrase referring to “at least one of” a list of itemsrefers to any combination of those items, including single members. Asan example, “at least one of: a, b, or c” is intended to cover: a, b, c,a-b, a-c, b-c, and a-b-c.

The various operations of methods described above may be performed byany suitable means capable of performing the operations, such as varioushardware and/or software component(s), circuits, and/or module(s).Generally, any operations illustrated in the Figures may be performed bycorresponding functional means capable of performing the operations.

The various illustrative logical blocks, modules and circuits describedin connection with the present disclosure may be implemented orperformed with a general purpose processor, a digital signal processor(DSP), an application specific integrated circuit (ASIC), a fieldprogrammable gate array signal (FPGA) or other programmable logic device(PLD), discrete gate or transistor logic, discrete hardware componentsor any combination thereof designed to perform the functions describedherein. A general purpose processor may be a microprocessor, but in thealternative, the processor may be any commercially available processor,controller, microcontroller or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration.

The steps of a method or algorithm described in connection with thepresent disclosure may be embodied directly in hardware, in a softwaremodule executed by a processor, or in a combination of the two. Asoftware module may reside in any form of storage medium that is knownin the art. Some examples of storage media that may be used includerandom access memory (RAM), read only memory (ROM), flash memory, EPROMmemory, EEPROM memory, registers, a hard disk, a removable disk, aCD-ROM and so forth. A software module may comprise a singleinstruction, or many instructions, and may be distributed over severaldifferent code segments, among different programs, and across multiplestorage media. A storage medium may be coupled to a processor such thatthe processor can read information from, and write information to, thestorage medium. In the alternative, the storage medium may be integralto the processor.

The methods disclosed herein comprise one or more steps or actions forachieving the described method. The method steps and/or actions may beinterchanged with one another without departing from the scope of theclaims. In other words, unless a specific order of steps or actions isspecified, the order and/or use of specific steps and/or actions may bemodified without departing from the scope of the claims.

The functions described may be implemented in hardware, software,firmware, or any combination thereof. If implemented in software, thefunctions may be stored or transmitted over as one or more instructionsor code on a computer-readable medium. Computer-readable media includeboth computer storage media and communication media including any mediumthat facilitates transfer of a computer program from one place toanother. A storage medium may be any available medium that can beaccessed by a computer. By way of example, and not limitation, suchcomputer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or otheroptical disk storage, magnetic disk storage or other magnetic storagedevices, or any other medium that can be used to carry or store desiredprogram code in the form of instructions or data structures and that canbe accessed by a computer. Also, any connection is properly termed acomputer-readable medium. For example, if the software is transmittedfrom a website, server, or other remote source using a coaxial cable,fiber optic cable, twisted pair, digital subscriber line (DSL), orwireless technologies such as infrared (IR), radio, and microwave, thenthe coaxial cable, fiber optic cable, twisted pair, DSL, or wirelesstechnologies such as infrared, radio, and microwave are included in thedefinition of medium. Disk and disc, as used herein, include compactdisc (CD), laser disc, optical disc, digital versatile disc (DVD),floppy disk, and Blu-ray® disc where disks usually reproduce datamagnetically, while discs reproduce data optically with lasers. Thus, insome aspects computer-readable media may comprise non-transitorycomputer-readable media (e.g., tangible media). In addition, for otheraspects computer-readable media may comprise transitorycomputer-readable media (e.g., a signal). Combinations of the aboveshould also be included within the scope of computer-readable media.

Thus, certain aspects may comprise a computer program product forperforming the operations presented herein. For example, such a computerprogram product may comprise a computer readable medium havinginstructions stored (and/or encoded) thereon, the instructions beingexecutable by one or more processors to perform the operations describedherein. For certain aspects, the computer program product may includepackaging material.

Software or instructions may also be transmitted over a transmissionmedium. For example, if the software is transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition oftransmission medium.

Further, it should be appreciated that modules and/or other appropriatemeans for performing the methods and techniques described herein can bedownloaded and/or otherwise obtained by a user terminal and/or basestation as applicable. For example, such a device can be coupled to aserver to facilitate the transfer of means for performing the methodsdescribed herein. Alternatively, various methods described herein can beprovided via storage means (e.g., RAM, ROM, a physical storage mediumsuch as a compact disc (CD) or floppy disk, etc.), such that a userterminal and/or base station can obtain the various methods uponcoupling or providing the storage means to the device. Moreover, anyother suitable technique for providing the methods and techniquesdescribed herein to a device can be utilized.

It is to be understood that the claims are not limited to the preciseconfiguration and components illustrated above. Various modifications,changes and variations may be made in the arrangement, operation anddetails of the methods and apparatus described above without departingfrom the scope of the claims.

While the foregoing is directed to aspects of the present disclosure,other and further aspects of the disclosure may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

The invention claimed is:
 1. An electrical circuit, comprising: aplurality of Retinal Ganglion Cell (RGC) circuits, wherein each of theRGC circuits generates, at an output, a sum of weighted inputs fromreceptor circuits associated with that RGC circuit; a plurality ofprimary visual cortex cell (V1) circuits, wherein each of the V1circuits generates another sum of weighted outputs of a subset of theRGC circuits; and a circuit configured to adjust weights applied on theoutputs for generating the other sum, wherein the adjustment of one ofthe weights is based on at least one of one of the outputs on which thatweight is applied or the other sum.
 2. The electrical circuit of claim1, wherein the adjustment of that weight is based on a sign of thatoutput and a sign of the other sum.
 3. The electrical circuit of claim1, wherein the adjustment of that weight is based on a sign of thatoutput and a value of the other sum.
 4. The electrical circuit of claim1, wherein: that weight is increased, if that output and the other sumare both positive or both negative, and that weight is decreased, if asign of that output and a sign of the other sum are different.
 5. Theelectrical circuit of claim 1, wherein that V1 circuit outputs a signal,if the other sum generated by that V1 circuit exceeds a threshold. 6.The electrical circuit of claim 1, wherein the circuit is alsoconfigured to adjust each of the weights by performing a binary shiftoperation.
 7. The electrical circuit of claim 1, wherein the inputs fromthe receptor circuits are weighted according to a Laplacian windowfunction.
 8. A method for implementing a neural system, comprising:generating, at an output of each Retinal Ganglion Cell (RGC) circuit ofa plurality of RGC circuits in the neural system, a sum of weightedinputs from receptor circuits associated with that RGC circuit;generating, by each primary visual cortex cell (V1) circuit of aplurality of V1 circuits in the neural system, another sum of weightedoutputs of a subset of the RGC circuits; and adjusting weights appliedon the outputs for generating the other sum, wherein the adjustment ofone of the weights is based on at least one of one of the outputs onwhich that weight is applied or the other sum.
 9. The method of claim 8,wherein the adjustment of that weight is based on a sign of that outputand a sign of the other sum.
 10. The method of claim 8, wherein theadjustment of that weight is based on a sign of that output and a valueof the other sum.
 11. The method of claim 8, wherein: that weight isincreased, if that output and the other sum are both positive or bothnegative, and that weight is decreased, if a sign of that output and asign of the other sum are different.
 12. The method of claim 8, furthercomprising: generating a signal at an output of that V1 circuit, if theother sum generated by that V1 circuit exceeds a threshold.
 13. Themethod of claim 8, wherein adjusting each of the weights comprises:performing a binary shift operation.
 14. The method of claim 8, whereinthe inputs from the receptor circuits are weighted according to aLaplacian window function.
 15. An apparatus, comprising: means forgenerating, at an output of each Retinal Ganglion Cell (RGC) circuit ofa plurality of RGC circuits in the apparatus, a sum of weighted inputsfrom receptor circuits associated with that RGC circuit; means forgenerating, by each primary visual cortex cell (V1) circuit of aplurality of V1 circuits in the apparatus, another sum of weightedoutputs of a subset of the RGC circuits; and means for adjusting weightsapplied on the outputs for generating the other sum, wherein theadjustment of one of the weights is based on at least one of one of theoutputs on which that weight is applied or the other sum.
 16. Theapparatus of claim 15, wherein the adjustment of that weight is based ona sign of that output and a sign of the other sum.
 17. The apparatus ofclaim 15, wherein the adjustment of that weight is based on a sign ofthat output and a value of the other sum.
 18. The method of claim 15,wherein: that weight is increased, if that output and the other sum areboth positive or both negative, and that weight is decreased, if a signof that output and a sign of the other sum are different.
 19. Theapparatus of claim 15, further comprising: means for generating a signalat an output of that V1 circuit, if the other sum generated by that V1circuit exceeds a threshold.
 20. The apparatus of claim 15, wherein themeans for adjusting each of the weights comprises: means for performinga binary shift operation.
 21. The apparatus of claim 15, wherein theinputs from the receptor circuits are weighted according to a Laplacianwindow function.